Setting a general background for my question:
We know that the equation of state for an ideal gas is given by:
- $p$ is the absolute pressure of the gas.
- $v$ is the volume per unit mass of the gas.
- $R$ is the gas constant.
- $T$ is the absolute temperature.
We also know that, following Maxwell equations, the internal energy solely depends on the temperature: $$e=e(T)$$
Introducing enthalpy ($h\equiv e+pv$) and using the equation of state for an ideal gas, we can conclude from Maxwell equations that the enthalpy also depends solely on the temperature: $$h=h(T)$$
The book I'm using to study Thermodynamics of propulsion, gives a word of warning:
Both the internal energy and the enthalpy can change in the complete absence of heat.
We are still considering ideal gases. However, heat is closely related to change in temperature, and both $e$ and $h$ depend solely on $T$.
My question might be considered a bit basic (I'm starting with Thermodynamics), but I can't quite understand the word of warning the authors gave. How is it possible that $h$ and $e$ change in complete absence of heat, if both depend on $T$? Can you give an example?
Trying to solve my own question:
One example I can think of where $e$ would change in absence of heat is when compressing a gas (I don't know if this is true at all). But I don't have a way to visualize the enthalpy.